code: def difference_function(x, n, tau_max):
      """
      Compute difference function of data x. This solution is implemented directly
      with Numpy fft.
  
  
      :param x: audio data
      :param n: length of data
      :param tau_max: integration window size
      :return: difference function
      :rtype: list
      """
  
      x = np.array(x, np.float64)
      w = x.size
      tau_max = min(tau_max, w)
      x_cumsum = np.concatenate((np.array([0.0]), (x * x).cumsum()))
      size = w + tau_max
      p2 = (size // 32).bit_length()
      nice_numbers = (16, 18, 20, 24, 25, 27, 30, 32)
      size_pad = min(
          x * 2**p2 for x in nice_numbers if x * 2**p2 >= size
      )
      fc = np.fft.rfft(x, size_pad)
      conv = np.fft.irfft(fc * fc.conjugate())[:tau_max]
      return (
          x_cumsum[w : w - tau_max : -1]
          + x_cumsum[w]
          - x_cumsum[:tau_max]
          - 2 * conv
      )
  
file_path: fairseq/examples/speech_synthesis/evaluation/eval_f0.py
imports: import numpy
  import os.path
  import torchaudio
  import tqdm
  from tabulate import tabulate
  from examples.speech_synthesis.utils import gross_pitch_error, voicing_decision_error, f0_frame_error
  from examples.speech_synthesis.evaluation.eval_sp import load_eval_spec
label_desc: Use image node_id 1 for calling a global function with example usage: difference_function(x, n, tau_max) and returns: unknown